Staff: Mentor

The stuff you put in LaTex isn't formatting, so I'll have to go with what I think the problem is.

You can change from the double integral over the region R to iterated integrals either by integrating with respect to y first and then x, or by integrating with respect to x first and then y. The region R is pretty simple, which makes matters simpler.

Using the same order that you chose, the inner integral is from y = 0 to y = 1, and the integrand is xy/(x^2 + y^2 + 1)^(1/2), and you're integrating with respect to y.

You can pull the factor of x outside the inner integral, since you're integrating w.r.t. y and x is constant on this strip.

A straightforward substitution will work: u = x^2 + y^2 + 1, so du = 2ydy. Remember, x is not varying, so x can be considered to be a constant.